Problem: Solve for $x$ and $y$ using elimination. ${-6x+y = -32}$ ${5x-y = 25}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-6x+y = -32}\thinspace$ to find $y$ ${-6}{(7)}{ + y = -32}$ $-42+y = -32$ $-42{+42} + y = -32{+42}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {5x-y = 25}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ - y = 25}$ ${y = 10}$